Re: Correlation ratio = eta-squared, or eta?


Bruce Weaver wrote:
I remember learning that "correlation ratio" is another name for
eta-squared, where eta-squared = 1 minus (SS_within/SS_Total) in a
one-way ANOVA design. (I just consulted my old Glass & Hopkins and
verified that my memory was not faulty.) However, when I Google on
<correlation ratio>, I get some pages that tell me correlation ratio =
eta, not eta-squared. Can anyone shed any light on this? Has the
definition changed? Do different fields use different terminology?

I ask because I was just revising some class notes, and was going to
write that eta-squared is sometimes called the "correlation ratio".

My recollection is that eta is the correlation ratio.

Checking Huberty (2002) which is to hand:

"Some years later, Pearson (1905) defined and labeled
η the correlation ratio. This coefficient was developed in the context
of multiple
data arrays (like groups in analysis of variance [ANOVA]) that
typically
suggested a nonlinear relationship between the grouping variable and
the
outcome variable. In 1924, Ronald A. Fisher (1890-1962) derived the
probability
distribution of η in the context of ANOVA. But the explicit analysis
connection between theANOVA F test and the correlation ratiowas not
made
until 1935 by Truman L. Kelley (1884-1961). (In an ANOVA context, the
η
value reflects the correlation between the grouping variable and the
outcome
variable.)"

Thom

.